next up previous
Next: Dirichlet series generating function Up: generating functions Previous: generating functions

Ordinary generating function

$\displaystyle G_0( \{a_n\}; X)=\sum_{n=0}^\infty a_n X^n $

EXAMPLE 01.2 (Examples of ordinary generating functions)  
  1. A generating function of a geometric progression:

    $\displaystyle \sum_{i=0}^n a^n X^n =\frac{1}{1-a X}. $

  2. A generating function of an arithmetic progression:

    $\displaystyle \sum_{i=0}^n (n+1) X^n =\frac{1}{(1- X)^2}. $


2013-04-05